"It's also not censorship for Twitter, a private company, to decide what it wants on its web pages and online services."
It is still censorship, just not government censorship. The definition from Webster does not specifically limit censorship to governments. The first paragraph from the ACLU makes it clear that censorship can be performed by governments or "private pressure groups". From the Global Internet Liberty Campaign "Not all censorship is equal, nor does all arise from government or external force. People self-censor all the time". The wired article has 6 tales of censorship, most with no government actions at all.
https://www.merriam-webster.com/dictionary/censorship
https://www.aclu.org/other/what-censorship
http://gilc.org/speech/osistudy/censorship/
https://www.wired.com/story/free-speech-issue-censorship/